It wouldn't be like going to Barca, it'd be like going to Atletico. And no, I wouldn't have a problem. Loyalty is something supporters and few footballers have in this sport. This isn't decades ago when the majority of players stayed at the same club for their entire careers.
Come on, don't be stupid. We like to make fun of Arsenal, but they're on a completely different level than Crystal Palace and West Ham and you know it. No two other London club plays in the Champions League. No two other London club is regularly in he top four. Would I have wanted him to go somewhere else? Of course! Do I hold it against him? No. He's played so many important games for this club, he's the greatest goalkeeper we've ever had. He deserves to stay in the city where he's settled and continue to play top football, because our club decided that he was getting too old and wanted to go for youth.
"Well Petr, you've done so much for this club. You'll be considered one of the best to play the game and you're our best ever goalkeeper. But now you must get the fuck out of London because our supporters may get pissy if you join a rival."
By the way, how have Arsenal improved with him? They still didn't win the league last season and many of them want him dropped this season.